Question: A circle has a sector with area $\dfrac{85}{8}\pi$ and central angle $153^\circ$. What is the area of the circle? ${25\pi}$ $\color{#9D38BD}{153^\circ}$ ${\dfrac{85}{8}\pi}$
The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{153^\circ}{360^\circ} = \dfrac{85}{8}\pi \div A_c$ $\dfrac{17}{40} = \dfrac{85}{8}\pi \div A_c$ $A_c \times \dfrac{17}{40} = \dfrac{85}{8}\pi$ $A_c = \dfrac{85}{8}\pi \times \dfrac{40}{17}$ $A_c = 25\pi$